Kawabata et al observed that, in pure rubbers, the degree of cross-link density effects both the first and second term of the strain energy function (
W function), as given by
W(I
1, I
2)=1/2νkT(I
1-3)+ν
1.5β(I
1, I
2)
where ν is the cross-link density. For reinforced rubbers, the
W function was found to given by
W(I
1, I
2)=1/2νkT(I
1-3)+ν
1.5β(I
1, I
2)+γ(I
1, φ, ν)
where γ is a function representing the effect of reinforcement, and is dependent on both ν and the volume fraction of carbon-black, φ. In this paper, we investigate the effect of cross-link density on the γ function. It is shown that the γ function for the SBR/carbon-black system is
γ(I
1, φ, ν)=A
1(φν)
1.5•(I
1-3)+A
2φν
2.5•Exp{1.35(I
1-3)}
where
A1 and
A2 are constants.
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